The subgroup permutability degree of projective special linear groups over fields of even characteristic

摘要

The subgroup permutability degree of a group G is defined as the probability that two subgroups of G permute, or equivalently that the product of two subgroups is again a subgroup. T?rn?uceanu asked in "Addendum to 'Subgroup commutativity degrees of finite groups'" (J. Algebra 337 (2011), 363-368) whether there exist families of groups other than dihedral, quasi-dihedral or generalised quaternion (all of 2-power cardinality), whose subgroup permutability degree tends to 0 as the size of the group tends to infinity. The purpose of this paper is to provide an affirmative answer for the family of projective special linear groups over fields of even characteristic by utilising a result of Dickson that gives a complete list of the subgroups of PSL_2(q).